Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Selective reflection from an atomic vapor in a pump-probe scheme

F. Schuller, Gerard Nienhuis, M. Ducloy

Published Jan 1, 1991• 29 citations
Publisher

Abstract

We evaluate the emission into a dielectric induced by the dipole polarization of an atomic vapor, in the case where two light beams are incident on the dielectric-vapor interface. These beams are a weak signal beam and a pump beam. Effects of spatial dispersion, arising from deexcitation of the vapor particles at collisions with the interface, are accounted for. The reflected radiation contains sub-Doppler structures arising from combinations of the effects of velocity-dependent transient behavior and the nonlinear response of the vapor. We express the modification of the signal-field reflection due to the pump field in terms of an effective susceptibility of the signal field. This susceptibility explicitly depends on the incidence angles and the frequencies of both beams. We present explicit simplified expressions for this effective susceptibility, valid in special cases. We also give some numerical results.

DOI
10.1103/physreva.43.443

Related papers

Nonlinear selective reflection in cascade three-level atomic systems

F. Schuller, O. Gorceix, M. Ducloy

We study the cascade three-level selective-reflection spectroscopy for normal incidence at a dielectric--atomic-vapor interface in a pump-probe scheme. Taking into account the effects of spatial dispersion arising from deexcitation by collisions with the interface and the transient response of atoms leaving the surface, we evaluate the modification of the probe-field reflection induced by the presence of the pump field in terms of a nonlocal nonlinear susceptibility. The dependence of this susceptibility on the probe frequency for various given pump frequencies is calculated. Sub-Doppler structures in the selective reflection spectrum are obtained and analyzed. Potential applications to the study of the interaction of highly excited atomic states with the surface are indicated.

Physical Review A•Jan 1, 1993•38 citations

Nonlinear selective reflection from an atomic vapor at arbitrary incidence angle

Gerard Nienhuis, F. Schuller, M. Ducloy

We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).

Physical Review A•Nov 1, 1988•116 citations

General theory of frequency modulated selective reflection. Influence of atom surface interactions

M. Ducloy, M. Fichet

We calculate the modulation of the reflection coefficient for a frequency-modulated (FM) light beam incident on the interface between a dielectric and an atomic vapor. The vapor is described as a gas of resonant, Doppler-broadened, two-level systems, with transition frequency and linewidth arbitrarily depending on the atom-dielectric distance. The atoms are supposed to get deexcited at collisions with the surface. The transient atomic response is calculated to first order in the incident field, for both incoming and desorbed atoms. The reflection coefficient, evaluated to first order in the vapor dipole polarization, leads to a formal expression of the reflectivity modulation, valid for arbitrary atom-surface interaction potentials. One first discusses the reflection signal in absence of wall interactions, for arbitrary modulation frequencies. At large frequencies, it allows one to monitor both vapor absorption and dispersion. Second, the formal theory is applied to the case of a Van der Waals-London surface attraction exerted on the atomic vapor. Both normal and oblique beam incidences are considered. One shows how the vapor dispersion signal is red-shifted and strongly distorted by the appearance of vapor-surface long-range interactions, and how it can be used to monitor these interactions. At non-normal incidences, the lineshapes get Doppler-broadened.

Journal de Physique II•Dec 1, 1991•57 citations

Selective reflection from a vapor of three-level atoms

Gerard Nienhuis, F. Schuller

We study internal selective reflection from a dielectric-vapor interface, where three levels of the vapor atoms in a \ensuremath{\Lambda} configuration are connected by two light frequencies. The reflectivity contains then both a sub-Doppler structure due to spatial dispersion in the boundary layer and the dark resonance arising from coherent population trapping. We derive analytical expressions for the reflectivity of either one of the two light beams. The contributions from atoms approaching or leaving the interface are strongly different, whereas they are identical for the case of two-state atoms.

Physical Review A•Aug 1, 1994•17 citations

Nonlinear effects in laser excitation of atomic gases in the vicinity of solid surfaces

T. A. Vartanyan, D. L. Lin

Understanding the processes underlying the optical excitation of atomic vapor in the vicinity of solid surfaces is of interest both from physical and technical points of view. Selective reflection spectra of laser light from an interface of a transparent dielectric material and resonant vapor are known to be Doppler-free and to provide important spectroscopic information about the atom-wall interaction. On the other hand, atomic vapors have such a large and fast nonlinear response on or near resonances that they are capable of processing signals and images with milliwatt lasers at a time scale of submicroseconds. In the present paper we investigate linear and nonlinear optical properties of a thin film of atomic vapor confined between two solid surfaces. Assuming two-level atoms, we solve the Maxwell- Bloch equations for light reflection from resonant atoms. The interaction between the resonant atoms and the wall is accounted for through the boundary conditions for all elements of density matrix. The transient polarization is shown to make an important contribution not only to the field structure in the vicinity of the wall but also to the interference pattern of the reflected field. It is found that the spectrum of reflection depends remarkably on the film thickness. Strong enhancement of signal is also found from this study and possible devices for the detection are discussed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 4, 1997•0 citations

Three-level nonlinear selective reflection at a glass–Cs-vapor interface

Anne Amy‐Klein, Solomon M. Saltiel, O. A. Rabi +1 more

We present an experimental study of nonlinear selective reflection at a dielectric--Cs-vapor interface, in a three-level cascade-up scheme. The nonlinear reflection at the Cs ${\mathit{D}}_{2}$ resonance line is monitored in the presence of resonant irradiation at 621 nm or 658 nm (6${\mathit{P}}_{3/2}$\ensuremath{\rightarrow}8${\mathit{D}}_{5/2}$,9${\mathit{S}}_{1/2}$). Experimental reflection spectra with either counterpropagating or copropagating light beams are analyzed and compared with the theoretical predictions of F. Schuller et al. [Phys. Rev. A 47, 519 (1993)]. For a blue-detuned pump and copropagating geometry an alternative type of three-level coherent reflection resonances, specifically associated with desorbing atoms, is observed. Also observed is the nonlinear reflection associated with the off-resonant, two-photon dispersion of atoms moving parallel to the window surface. Probe beam saturation is responsible for the appearance of additional resonant features in reflection spectra. Finally we analyze crossover spectral resonances which arise from nondegenerate, four-wave-mixing processes induced by the combined influence of counterpropagating pump and probe beams, and the pump beam being partially reflected by the window.

Physical Review A•Oct 1, 1995•13 citations
We evaluate the emission into a dielectric induced by the dipole polarization of an atomic vapor, in the case where two light beams are incident on the dielectric-vapor interface. These beams are a weak signal beam and a pump beam. Effects of spatial dispersion, arising from deexcitation of the vapor particles at collisions with the interface, are accounted for. The reflected radiation contains sub-Doppler structures arising from combinations of the effects of velocity-dependent transient behavior and the nonlinear response of the vapor. We express the modification of the signal-field reflection due to the pump field in terms of an effective susceptibility of the signal field. This susceptibility explicitly depends on the incidence angles and the frequencies of both beams. We present explicit simplified expressions for this effective susceptibility, valid in special cases. We also give some numerical results.
We study the cascade three-level selective-reflection spectroscopy for normal incidence at a dielectric--atomic-vapor interface in a pump-probe scheme. Taking into account the effects of spatial dispersion arising from deexcitation by collisions with the interface and the transient response of atoms leaving the surface, we evaluate the modification of the probe-field reflection induced by the presence of the pump field in terms of a nonlocal nonlinear susceptibility. The dependence of this susceptibility on the probe frequency for various given pump frequencies is calculated. Sub-Doppler structures in the selective reflection spectrum are obtained and analyzed. Potential applications to the study of the interaction of highly excited atomic states with the surface are indicated.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
We calculate the modulation of the reflection coefficient for a frequency-modulated (FM) light beam incident on the interface between a dielectric and an atomic vapor. The vapor is described as a gas of resonant, Doppler-broadened, two-level systems, with transition frequency and linewidth arbitrarily depending on the atom-dielectric distance. The atoms are supposed to get deexcited at collisions with the surface. The transient atomic response is calculated to first order in the incident field, for both incoming and desorbed atoms. The reflection coefficient, evaluated to first order in the vapor dipole polarization, leads to a formal expression of the reflectivity modulation, valid for arbitrary atom-surface interaction potentials. One first discusses the reflection signal in absence of wall interactions, for arbitrary modulation frequencies. At large frequencies, it allows one to monitor both vapor absorption and dispersion. Second, the formal theory is applied to the case of a Van der Waals-London surface attraction exerted on the atomic vapor. Both normal and oblique beam incidences are considered. One shows how the vapor dispersion signal is red-shifted and strongly distorted by the appearance of vapor-surface long-range interactions, and how it can be used to monitor these interactions. At non-normal incidences, the lineshapes get Doppler-broadened.
We study internal selective reflection from a dielectric-vapor interface, where three levels of the vapor atoms in a \ensuremath{\Lambda} configuration are connected by two light frequencies. The reflectivity contains then both a sub-Doppler structure due to spatial dispersion in the boundary layer and the dark resonance arising from coherent population trapping. We derive analytical expressions for the reflectivity of either one of the two light beams. The contributions from atoms approaching or leaving the interface are strongly different, whereas they are identical for the case of two-state atoms.
Understanding the processes underlying the optical excitation of atomic vapor in the vicinity of solid surfaces is of interest both from physical and technical points of view. Selective reflection spectra of laser light from an interface of a transparent dielectric material and resonant vapor are known to be Doppler-free and to provide important spectroscopic information about the atom-wall interaction. On the other hand, atomic vapors have such a large and fast nonlinear response on or near resonances that they are capable of processing signals and images with milliwatt lasers at a time scale of submicroseconds. In the present paper we investigate linear and nonlinear optical properties of a thin film of atomic vapor confined between two solid surfaces. Assuming two-level atoms, we solve the Maxwell- Bloch equations for light reflection from resonant atoms. The interaction between the resonant atoms and the wall is accounted for through the boundary conditions for all elements of density matrix. The transient polarization is shown to make an important contribution not only to the field structure in the vicinity of the wall but also to the interference pattern of the reflected field. It is found that the spectrum of reflection depends remarkably on the film thickness. Strong enhancement of signal is also found from this study and possible devices for the detection are discussed.
We present an experimental study of nonlinear selective reflection at a dielectric--Cs-vapor interface, in a three-level cascade-up scheme. The nonlinear reflection at the Cs D2{\mathit{D}}_{2}D2​ resonance line is monitored in the presence of resonant irradiation at 621 nm or 658 nm (6P3/2{\mathit{P}}_{3/2}P3/2​\ensuremath{\rightarrow}8D5/2{\mathit{D}}_{5/2}D5/2​,9S1/2{\mathit{S}}_{1/2}S1/2​). Experimental reflection spectra with either counterpropagating or copropagating light beams are analyzed and compared with the theoretical predictions of F. Schuller et al. [Phys. Rev. A 47, 519 (1993)]. For a blue-detuned pump and copropagating geometry an alternative type of three-level coherent reflection resonances, specifically associated with desorbing atoms, is observed. Also observed is the nonlinear reflection associated with the off-resonant, two-photon dispersion of atoms moving parallel to the window surface. Probe beam saturation is responsible for the appearance of additional resonant features in reflection spectra. Finally we analyze crossover spectral resonances which arise from nondegenerate, four-wave-mixing processes induced by the combined influence of counterpropagating pump and probe beams, and the pump beam being partially reflected by the window.